Calcula la derivada de la funcion f(x)=2^x9

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$\left(x\right)=2^x\cdot\:9$(x)=2x· 9

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$\mathrm{Prepare}\:\left(x\right)=2^x9\:\mathrm{for\:Lambert\:form}:\quad xe^{-\ln\left(2\right)x}=9$Prepare (x)=2x9 for Lambert form:    xe−ln(2)x=9

$\mathrm{Rewrite\:the\:equation\:with\:}-x\ln\left(2\right)=u\mathrm{\:and\:}x=-\frac{u}{\ln\left(2\right)}$Rewrite the equation with −xln(2)=u and x=−

u

ln(2)

$\left(-\frac{u}{\ln\left(2\right)}\right)e^u=9$(−

u

ln(2) )eu=9

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$\mathrm{Rewrite}\:\left(-\frac{u}{\ln\left(2\right)}\right)e^u=9\:\mathrm{in\:Lambert\:form}:\quad e^uu=-9\ln\left(2\right)$Rewrite (−

u

ln(2) )eu=9 in Lambert form:    euu=−9ln(2)

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$\mathrm{Solve\:}\:e^uu=-9\ln\left(2\right):\quad\mathrm{No\:Solution\:for}\:u\in\mathbb{R}$Solve  euu=−9ln(2):    No Solution for u∈ℝ

$\mathrm{No\:Solution\:for}\:x\in\mathbb{R}$

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you need to show the graph

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the expected value of the random variable : 0, 1 and 2

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